In this second resubmission of a 5-year competing renewal, we have carefully addressed a new set of concerns raised by the reviewers including more details on the MAP-EM algorithm, the optimization methods using simulated 4D gated SPECT and PET data, validation method for the proposed 4D observer model and the clinical evaluation study. During the current grant, we have developed improved 4D image reconstruction methods for gated myocardial perfusion (GMP) SPECT that provide better time resolution through the use of more frames per cardiac cycle without degrading the noise characteristics of the images. This has the potential to provide improved visualization of regional myocardial wall motion abnormalities. We have developed methods to determine the motion vector fields of the myocardium from the GMP SPECT data using known cardiac material properties and an average motion model of the heart as the initial estimate. Also, we have developed task-based methods using the CHO and ROC methodology to optimize and evaluate these new techniques using simulated data from populations of 4D NCAT phantoms that realistically model anatomical and physiological variations found in clinical data. Based on encouraging results from this study, we propose to continue our investigation into 4D image reconstruction methods to further improve the quality and quantitative accuracy of 4D GMP ECT images. We propose to extend the investigation to GMP PET using Rb-82. Similar to the current study on GMP SPECT, we propose to initially optimize and evaluate the data acquisition and 4D image reconstruction methods for GMP PET using realistic computer simulated data. A hybrid Monte Carlo technique developed in our laboratory will be used to provide efficient generation of GMP PET data from populations of the 4D NCAT phantoms with accurate modeling of the PET system geometries and detector configuration. We will then validate the data acquisition and optimize the 4D image reconstruction methods through experiments on clinical systems using a dynamic cardiac physical phantom. With the support of GE Healthcare, we propose to implement listmode data acquisition capabilities in both the GE SPECT/CT and PET/CT clinical systems used in this study. Task-based evaluation methods using CHO and ROC methodology will be applied to evaluate improvements in detecting regional wall motion abnormalities in GMP SPECT and PET images obtained from the phantom data. Finally, we propose to initiate evaluation of the 4D image reconstruction methods using clinical GMP SPECT and PET data acquired using the listmode data acquisition. We will compare evaluation results from the CHO and human observers using simulated data. We will also compare evaluation results from the simulation study and clinical study using trained physicians. These results will allow assessment of the utility of mathematical observers in task-based evaluation of 4D GMP SPECT and PET imaging techniques.